1
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Question

# A solid sphere of uniform density and radius R applied a gravitational force of attraction equal to F1 on a particle placed at a distance 2R from the centre of the sphere. A spherical cavity of radius R/2 is now made in the sphere as shown in the figure. The sphere with the cavity now applied a gravitational force F2 on the same particles. The ratio F1/F2 is?

A
12
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B
34
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C
78
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D
97
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Solution

## The correct option is D 97F1=P43πR3(2R)2F2=P43πR3(2R)2−P43π(R2)3(23R)2=P43π736R⇒F1F2=14×367=97

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